Reports like these are fun. The video has a sincerity to it, the person who filmed it doesn't come across as a hoaxer or someone who is anomaly hunting. Here's the video itself, posted by a family member:

My favorite thing about this video is that we get a sense of distance, and from that, a sense of scale. The object clearly passes behind the statue.

The above two images show it passing behind the head. The video follows it on past the arm as well. Toward the end of the video, the object appears to stop relative to the statue for a time.

To my eye, the object is most likely some form of solar balloon. A solar balloon is a balloon that achieves its lift via solar heating. It's a sealed form of a hot air balloon. You can see a some example images here.

Judging by its relative speed, I don't think it is very far behind the statue, or very high in the air. It's hard to say for sure without knowing the size of the object. It is possible to see the object change its shape, from more circular to more oval and back. This is consistent with a solar balloon.

The object's motion is consistent with a wind-borne balloon as well, even given the apparent stop it does. It is unclear what the higher-level winds are doing at that moment. It's quite plausible that there was a gust or a brief change in the winds that caused the balloon to either appear to stop or to move in a direction toward or away from the camera. If it was also rising or sinking at the same time, its apparent size could stay the same.

Of course, we don't actually know what it is, but I'm going with balloon. What do y'all think?